The equation of a parabola is given.

Steps to finding the directrix given the equation of the parabola:
1) Find p-value
2) Find vertex
3) Sketch a diagram and label it (optional, but helpful)
steps 1 and 2 can be done in any order

y=1/2x^2+6x+24     factor out the 1/2

y  = (1/2) [ x^2 + 12x + 48  ] completet te square on x

y  = (1/2)  [ x^2  + 12 x  + 36  + 48 - 36 ]    factor the first three terms in the parenthses, simplify the rest

y =  (1/2)  [ ( x + 6)^2    + 12 ]      

y  =(1/2) ( x + 6)^2  + 6    

y - 6  =  (1/2)( x + 6)^2    multiply both sides by 2

2 ( y - 6)  = (x+ 6)^2

The vertex  is   ( --6, 6)

To find the directrix

4p  = 2

p = 2/4

p =  1/2

The parabola turns upward...so the  directrix   is   y  = 6  - 1/2   =  5.5